EXECUTIVE SUMMARY
The strength of a nation and the wellbeing of its citizens are determined to a substantial degree by its technological development and its level of economic organization. The starting point of this report is the broad consensus that advanced technology is a vital component of economic competitiveness. Within this framework, this report documents the importance of quantitative reasoning, supported by computational and mathematical models, to all aspects of the complete product cycle and to the economic competitiveness of U.S. industry.

The quantitative, mathematical and computational approach is enabling, making possible accomplishments that would otherwise not occur. The design of fuelefficient transonic aircraft is an example, as are the statistical design of experiments in the drug industry, and image reconstruction and enhancement for medical tomography.

The quantitative approach leads to successive and dramatic improvement in the design and manufacture of new goods and services. The rapid evolution of computer technology, the design of semiconductor devices, and the design of optical lithography used in the manufacture of these devices are examples. Improved oil recovery derives from models of flows in porous media, the importance of which is underscored by potential disruptions to international oil supplies.

The quantitative approach is essential to achieving, maintaining, and improving product quality. Tough international competition for the best engineering design of very largescale integrated (VLSI) circuits (offline quality control) and in the maintenance

of quality through process control (online quality control) reflects the application of this approach.

The quantitative approach addresses novel problems and objectives. The automobile engine has been extensively redesigned for better emission control and fuel efficiency on the basis of models of the combustion process. Computerbased justintime (JIT) inventory management, computerbased optimized pattern layout, and computeraided design offer the possibility of a newly competitive posture for a U.S.based apparel industry.

This approach is an ongoing and longterm process. To compete successfully in the global marketplace requires a continuous supply of highvalueadded products and, therefore, a national emphasis on high technology. There is no serious challenge to the validity or the success of this approach, nor to the requirement for a strong technology base, which this strategy implies.
Manufacturing is the area in which international economic competition is most intense. It plays the dominant role (approximately 60 percent) in world trade. For this reason, the advanced technology and competitiveness of the manufacturing process are important concerns of this report. Service is the larger part of the U.S. economy (70 percent), and it represents a growing portion of the export sector. Efficiency gains will be greatly multiplied if they are realized in this sector as well. Thus this report also discusses the role of technology and quantitative thinking in the service sector. Technology and quantitative thinking contribute to the competitiveness of all economic sectors.
In addition to the creation of technology, its transfer into new goods and services is of central importance. In view of the continuous web of ideas that make up the intellectual life of our nation, it seems most practical to create technology and to promote its transfer broadly for all segments of the economy, even though the concerns of this report relate most directly to support for the manufacturing sector.
Technology transfer will have occurred when a new idea, a new method, or a new process has been successfully incorporated into a product or service. Active cooperation among the research group, the
design engineers, and the manufacturing team presents the ideal climate for rapid technology transfer. The Board on Mathematical Sciences views advanced technology and its transfer as essential for the economic viability and leadership of our nation, and deems it the responsiblity of all participants, users and producers of the technology base, to foster that transfer actively.
Findings

The mathematical sciences are vital to economic competitiveness. They are a critical, generic, enabling technology.
This principal finding is elaborated further by these observations:

Applications of the mathematical sciences arise in all aspects of the product cycle and across the technology base.

Applications also arise from highly diverse areas of the mathematical sciences; they depend on the vitality of research in the mathematical sciences and draw on this research as a technology base.

Computation and modeling recur as central themes. They are a primary route for technology transfer from the mathematical sciences.

Technology transfer, from the research to the industrial sector, is of critical importance for the enhancement of economic competitiveness.

In the mathematical sciences (as elsewhere), technology transfer occurs seriously below its potential. The transfer of technology will be accomplished best if the creators of technology assume the primary responsibility for its transfer. Also helpful is an atmosphere of cooperation among the industrial, governmental, and academic sectors, an atmosphere in which the central importance of technology transfer is clearly understood by the participants in the process.

Technology transfer, computational and mathematical modeling, and education have an importance to economic competitiveness that is very large relative to the recognition given to these activities by the academic mathematical sciences community.

Manpower and technical training are also crucial for economic competitiveness. The mathematical sciences community has a significant responsibility in this area.
The ability of the mathematical sciences community to deliver shortterm results with any degree of consistency depends crucially on healthy support for its longterm development. Engineering and manufacturing research and design depend heavily on computational and mathematical modeling. The mathematical sciences community has the primary responsibility for the collegiate mathematics education of engineers and scientists and has taken a leadership role in efforts to revitalize mathematics education at all levels. These three issues, longterm health and renewal of the mathematical sciences community, computation and mathematical modeling, and education and manpower training, have been considered in highlevel policy studies (see Appendix B for references). The recommendations in this report build on and supplement these studies, and the board specifically endorses the recommendations in the earlier reports.
Recommendations
This report makes two primary recommendations:

The board recommends that the mathematical sciences community significantly increase its role in the transfer of mathematical sciences technology.

The board calls on the mathematical sciences community to put far greater emphasis on and give greater career recognition to activities connected with computational and mathematical modeling, technology transfer, and education.
To ensure that technology transfer occurs, mathematical scientists, engineers, manufacturers, and business leaders must accept the task to be accomplished and plan for the result.
Computational and mathematical modeling, technology transfer, and education have a critical and direct connection to economic competitiveness, a connection that should be reflected in the recognition given these activities by the mathematical sciences community. Specific actions, endorsed by this report, for carrying out its two primary recommendations include the following:

Federal and state agencies should ensure that investments in research to improve productivity include the necessary involvement and support of the mathematical sciences.

Programs in industrial mathematics, jointly supported by industry and government, should be established in our colleges and universities and should include grants for small science and for individual investigators.
The economic competitiveness of the United States can be substantially improved by increased involvement of the mathematical sciences community. Numerous agencies currently sponsor programs that have successfully encouraged interaction between academic and government laboratory researchers. This report proposes a similar effort to stimulate increased interaction between universities and industry.
Federally funded science and technology centers already have a mandate for technology transfer. However, many industrial problems in mathematics are of moderate size, appropriate to small science and individual investigators. A formal program in industrial mathematics should therefore take advantage of the contributions that small science and individual investigators can make.

The board urges that strong and meaningful consideration for hiring, retention, promotion, and tenure be given for achievements in research and education supporting industrial mathematics. The emphasis given to computational mathematics, modeling, and applications should be in balance with that accorded to other areas of mathematics.

The board calls on university administrators to encourage adoption by their mathematical sciences units of criteria and procedures that promote strengthening of the ties between universities and industry.

Our national requirements for the creation of new mathematical sciences technology, as well as for effective access to this technology, call for a balance between theory and applications.

The board recommends that industry, government, and university cooperative research and education programs be encouraged and funded.
Cooperation among industry, government, and universities benefits all three. Such cooperation can take many forms, some of which, from the simple consultant relationship to the formation of industrial consortia, are mentioned in this report. Often such cooperation leads to employment for students, after graduation, by the industrial firm. At this point, an important step in completing technology transfer to the industrial sector has taken place.

The board recommends development of course materials to support the teaching of modeling and of industrial applications of mathematics.
The purpose of this course material would be to narrow the gap between academic mathematics and the industrial uses of mathematics, i.e, problem solving and modeling. The course material should broaden the students' intellectual horizons as well as their technical training. It should increase their potential usefulness in an industrial organization and should increase their ability, as future teachers of mathematics to engineers, to motivate the use of mathematics in an industrial context.

The board urges the mathematical sciences professional societies to promote intellectual activity in problem solving and modeling to strengthen the industrial use of mathematics.
Technology transfer can occur only with the full support of the people who are actively engaged in the process. The board proposes that the mathematical professional societies include technology transfer within their mission and encourage, through workshops, minisymposia, and plenary lectures, more interaction among mathematicians in industry, universities, and government laboratories. Special conferences on theoretical areas of mathematics could include the industrial
perspective as well. Mathematicians in industry should be encouraged to serve in larger numbers on the editorial boards of professional journals. Much of this framework is in place already, but the evident need to improve on the rate and calibre of technology transfer implies that increased attention to these issues is imperative.
Conclusions
Our industrial environment is undergoing rapid change. The mathematical sciences community can play a significant role in promoting this change in the United States by becoming an active partner in this process.
From engineering design and research to management and organizational structures to the control of smart machines and robots, the computer is leading a revolution that vitally affects the competitiveness of industry and of our entire society. The mathematical sciences are at the basis of many of those changes, and they provide a crucial technology in effecting this revolution. The continuing increase in the range of human and technological activities that can be described in mathematical terms is part of this revolution. Mathematics acts, and achieves its value, through its ability to organize and structure knowledge. The role of the mathematical sciences as a technology is not recognized, nor is the full importance of its role as a force for technological change and industrial competitiveness. This central fact is the basis for this report.